A graph \(G = (V, E)\)  is an interval graph if one can map each vertex into an interval on the real line so that any two vertices are adjacent if and only if their corresponding intervals intersect. Such a mapping of vertices into an interval on the real line is called an interval representation of \(G\). The study of interval graphs was motivated by the study of the famous molecular biologist Benzer [1]} in 1959. Since then interval graphs has been widely used in molecular biology and genetics, particularly for DNA sequencing. Different variations of interval graphs have been used to model different scenarios arising in the area of DNA sequencing. Literature on the applications of different variations of interval graphs can be found in [2]}, [3]}, [4]}.
